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Simplifying 2[7 + -6(1 + -1n)] + 9 = -20 + 4[6(n + 1) + -3n] 2[7 + (1 * -6 + -1n * -6)] + 9 = -20 + 4[6(n + 1) + -3n] 2[7 + (-6 + 6n)] + 9 = -20 + 4[6(n + 1) + -3n] Combine like terms: 7 + -6 = 1 2[1 + 6n] + 9 = -20 + 4[6(n + 1) + -3n] [1 * 2 + 6n * 2] + 9 = -20 + 4[6(n + 1) + -3n] [2 + 12n] + 9 = -20 + 4[6(n + 1) + -3n] Reorder the terms: 2 + 9 + 12n = -20 + 4[6(n + 1) + -3n] Combine like terms: 2 + 9 = 11 11 + 12n = -20 + 4[6(n + 1) + -3n] Reorder the terms: 11 + 12n = -20 + 4[6(1 + n) + -3n] 11 + 12n = -20 + 4[(1 * 6 + n * 6) + -3n] 11 + 12n = -20 + 4[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 11 + 12n = -20 + 4[6 + 3n] 11 + 12n = -20 + [6 * 4 + 3n * 4] 11 + 12n = -20 + [24 + 12n] Combine like terms: -20 + 24 = 4 11 + 12n = 4 + 12n Add '-12n' to each side of the equation. 11 + 12n + -12n = 4 + 12n + -12n Combine like terms: 12n + -12n = 0 11 + 0 = 4 + 12n + -12n 11 = 4 + 12n + -12n Combine like terms: 12n + -12n = 0 11 = 4 + 0 11 = 4 Solving 11 = 4 Couldn't find a variable to solve for. This equation is invalid, the left and right sides are not equal, therefore there is no solution.
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